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<div class="subTitle">org.apache.commons.math3.geometry.euclidean.twod.hull</div>
<h2 title="Class MonotoneChain" class="title">Class MonotoneChain</h2>
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<li>org.apache.commons.math3.geometry.euclidean.twod.hull.MonotoneChain</li>
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<dt>All Implemented Interfaces:</dt>
<dd><a href="../../../../../../../../org/apache/commons/math3/geometry/euclidean/twod/hull/ConvexHullGenerator2D.html" title="interface in org.apache.commons.math3.geometry.euclidean.twod.hull">ConvexHullGenerator2D</a>, <a href="../../../../../../../../org/apache/commons/math3/geometry/hull/ConvexHullGenerator.html" title="interface in org.apache.commons.math3.geometry.hull">ConvexHullGenerator</a>&lt;<a href="../../../../../../../../org/apache/commons/math3/geometry/euclidean/twod/Euclidean2D.html" title="class in org.apache.commons.math3.geometry.euclidean.twod">Euclidean2D</a>,<a href="../../../../../../../../org/apache/commons/math3/geometry/euclidean/twod/Vector2D.html" title="class in org.apache.commons.math3.geometry.euclidean.twod">Vector2D</a>&gt;</dd>
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<pre>public class <span class="strong">MonotoneChain</span>
extends <a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true" title="class or interface in java.lang">Object</a></pre>
<div class="block">Implements Andrew's monotone chain method to generate the convex hull of a finite set of
 points in the two-dimensional euclidean space.
 <p>
 The runtime complexity is O(n log n), with n being the number of input points. If the
 point set is already sorted (by x-coordinate), the runtime complexity is O(n).
 <p>
 The implementation is not sensitive to collinear points on the hull. The parameter
 <code>includeCollinearPoints</code> allows to control the behavior with regard to collinear points.
 If <code>true</code>, all points on the boundary of the hull will be added to the hull vertices,
 otherwise only the extreme points will be present. By default, collinear points are not added
 as hull vertices.
 <p>
 The <code>tolerance</code> parameter (default: 1e-10) is used as epsilon criteria to determine
 identical and collinear points.</div>
<dl><dt><span class="strong">Since:</span></dt>
  <dd>3.3</dd>
<dt><span class="strong">See Also:</span></dt><dd><a href="http://en.wikibooks.org/wiki/Algorithm_Implementation/Geometry/Convex_hull/Monotone_chain">
 Andrew's monotone chain algorithm (Wikibooks)</a></dd></dl>
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<th class="colOne" scope="col">Constructor and Description</th>
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<td class="colOne"><code><strong><a href="../../../../../../../../org/apache/commons/math3/geometry/euclidean/twod/hull/MonotoneChain.html#MonotoneChain()">MonotoneChain</a></strong>()</code>
<div class="block">Create a new MonotoneChain instance.</div>
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<td class="colOne"><code><strong><a href="../../../../../../../../org/apache/commons/math3/geometry/euclidean/twod/hull/MonotoneChain.html#MonotoneChain(boolean)">MonotoneChain</a></strong>(boolean&nbsp;includeCollinearPoints)</code>
<div class="block">Create a new MonotoneChain instance.</div>
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<td class="colOne"><code><strong><a href="../../../../../../../../org/apache/commons/math3/geometry/euclidean/twod/hull/MonotoneChain.html#MonotoneChain(boolean,%20double)">MonotoneChain</a></strong>(boolean&nbsp;includeCollinearPoints,
             double&nbsp;tolerance)</code>
<div class="block">Create a new MonotoneChain instance.</div>
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<td class="colFirst"><code><a href="http://docs.oracle.com/javase/7/docs/api/java/util/Collection.html?is-external=true" title="class or interface in java.util">Collection</a>&lt;<a href="../../../../../../../../org/apache/commons/math3/geometry/euclidean/twod/Vector2D.html" title="class in org.apache.commons.math3.geometry.euclidean.twod">Vector2D</a>&gt;</code></td>
<td class="colLast"><code><strong><a href="../../../../../../../../org/apache/commons/math3/geometry/euclidean/twod/hull/MonotoneChain.html#findHullVertices(java.util.Collection)">findHullVertices</a></strong>(<a href="http://docs.oracle.com/javase/7/docs/api/java/util/Collection.html?is-external=true" title="class or interface in java.util">Collection</a>&lt;<a href="../../../../../../../../org/apache/commons/math3/geometry/euclidean/twod/Vector2D.html" title="class in org.apache.commons.math3.geometry.euclidean.twod">Vector2D</a>&gt;&nbsp;points)</code>
<div class="block">Find the convex hull vertices from the set of input points.</div>
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<td class="colFirst"><code><a href="../../../../../../../../org/apache/commons/math3/geometry/euclidean/twod/hull/ConvexHull2D.html" title="class in org.apache.commons.math3.geometry.euclidean.twod.hull">ConvexHull2D</a></code></td>
<td class="colLast"><code><strong><a href="../../../../../../../../org/apache/commons/math3/geometry/euclidean/twod/hull/MonotoneChain.html#generate(java.util.Collection)">generate</a></strong>(<a href="http://docs.oracle.com/javase/7/docs/api/java/util/Collection.html?is-external=true" title="class or interface in java.util">Collection</a>&lt;<a href="../../../../../../../../org/apache/commons/math3/geometry/euclidean/twod/Vector2D.html" title="class in org.apache.commons.math3.geometry.euclidean.twod">Vector2D</a>&gt;&nbsp;points)</code>
<div class="block">Builds the convex hull from the set of input points.</div>
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<tr class="altColor">
<td class="colFirst"><code>double</code></td>
<td class="colLast"><code><strong><a href="../../../../../../../../org/apache/commons/math3/geometry/euclidean/twod/hull/MonotoneChain.html#getTolerance()">getTolerance</a></strong>()</code>
<div class="block">Get the tolerance below which points are considered identical.</div>
</td>
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<td class="colFirst"><code>boolean</code></td>
<td class="colLast"><code><strong><a href="../../../../../../../../org/apache/commons/math3/geometry/euclidean/twod/hull/MonotoneChain.html#isIncludeCollinearPoints()">isIncludeCollinearPoints</a></strong>()</code>
<div class="block">Returns if collinear points on the hull will be added as hull vertices.</div>
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<h3>Methods inherited from class&nbsp;java.lang.<a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true" title="class or interface in java.lang">Object</a></h3>
<code><a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true#clone()" title="class or interface in java.lang">clone</a>, <a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true#equals(java.lang.Object)" title="class or interface in java.lang">equals</a>, <a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true#finalize()" title="class or interface in java.lang">finalize</a>, <a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true#getClass()" title="class or interface in java.lang">getClass</a>, <a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true#hashCode()" title="class or interface in java.lang">hashCode</a>, <a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true#notify()" title="class or interface in java.lang">notify</a>, <a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true#notifyAll()" title="class or interface in java.lang">notifyAll</a>, <a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true#toString()" title="class or interface in java.lang">toString</a>, <a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true#wait()" title="class or interface in java.lang">wait</a>, <a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true#wait(long)" title="class or interface in java.lang">wait</a>, <a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true#wait(long,%20int)" title="class or interface in java.lang">wait</a></code></li>
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<h4>MonotoneChain</h4>
<pre>public&nbsp;MonotoneChain()</pre>
<div class="block">Create a new MonotoneChain instance.</div>
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<h4>MonotoneChain</h4>
<pre>public&nbsp;MonotoneChain(boolean&nbsp;includeCollinearPoints)</pre>
<div class="block">Create a new MonotoneChain instance.</div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>includeCollinearPoints</code> - whether collinear points shall be added as hull vertices</dd></dl>
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<h4>MonotoneChain</h4>
<pre>public&nbsp;MonotoneChain(boolean&nbsp;includeCollinearPoints,
             double&nbsp;tolerance)</pre>
<div class="block">Create a new MonotoneChain instance.</div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>includeCollinearPoints</code> - whether collinear points shall be added as hull vertices</dd><dd><code>tolerance</code> - tolerance below which points are considered identical</dd></dl>
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<a name="findHullVertices(java.util.Collection)">
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<h4>findHullVertices</h4>
<pre>public&nbsp;<a href="http://docs.oracle.com/javase/7/docs/api/java/util/Collection.html?is-external=true" title="class or interface in java.util">Collection</a>&lt;<a href="../../../../../../../../org/apache/commons/math3/geometry/euclidean/twod/Vector2D.html" title="class in org.apache.commons.math3.geometry.euclidean.twod">Vector2D</a>&gt;&nbsp;findHullVertices(<a href="http://docs.oracle.com/javase/7/docs/api/java/util/Collection.html?is-external=true" title="class or interface in java.util">Collection</a>&lt;<a href="../../../../../../../../org/apache/commons/math3/geometry/euclidean/twod/Vector2D.html" title="class in org.apache.commons.math3.geometry.euclidean.twod">Vector2D</a>&gt;&nbsp;points)</pre>
<div class="block">Find the convex hull vertices from the set of input points.</div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>points</code> - the set of input points</dd>
<dt><span class="strong">Returns:</span></dt><dd>the convex hull vertices in CCW winding</dd></dl>
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<h4>getTolerance</h4>
<pre>public&nbsp;double&nbsp;getTolerance()</pre>
<div class="block">Get the tolerance below which points are considered identical.</div>
<dl><dt><span class="strong">Returns:</span></dt><dd>the tolerance below which points are considered identical</dd></dl>
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<pre>public&nbsp;boolean&nbsp;isIncludeCollinearPoints()</pre>
<div class="block">Returns if collinear points on the hull will be added as hull vertices.</div>
<dl><dt><span class="strong">Returns:</span></dt><dd><code>true</code> if collinear points are added as hull vertices, or <code>false</code>
 if only extreme points are present.</dd></dl>
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<h4>generate</h4>
<pre>public&nbsp;<a href="../../../../../../../../org/apache/commons/math3/geometry/euclidean/twod/hull/ConvexHull2D.html" title="class in org.apache.commons.math3.geometry.euclidean.twod.hull">ConvexHull2D</a>&nbsp;generate(<a href="http://docs.oracle.com/javase/7/docs/api/java/util/Collection.html?is-external=true" title="class or interface in java.util">Collection</a>&lt;<a href="../../../../../../../../org/apache/commons/math3/geometry/euclidean/twod/Vector2D.html" title="class in org.apache.commons.math3.geometry.euclidean.twod">Vector2D</a>&gt;&nbsp;points)
                      throws <a href="../../../../../../../../org/apache/commons/math3/exception/NullArgumentException.html" title="class in org.apache.commons.math3.exception">NullArgumentException</a>,
                             <a href="../../../../../../../../org/apache/commons/math3/exception/ConvergenceException.html" title="class in org.apache.commons.math3.exception">ConvergenceException</a></pre>
<div class="block">Builds the convex hull from the set of input points.</div>
<dl>
<dt><strong>Specified by:</strong></dt>
<dd><code><a href="../../../../../../../../org/apache/commons/math3/geometry/euclidean/twod/hull/ConvexHullGenerator2D.html#generate(java.util.Collection)">generate</a></code>&nbsp;in interface&nbsp;<code><a href="../../../../../../../../org/apache/commons/math3/geometry/euclidean/twod/hull/ConvexHullGenerator2D.html" title="interface in org.apache.commons.math3.geometry.euclidean.twod.hull">ConvexHullGenerator2D</a></code></dd>
<dt><strong>Specified by:</strong></dt>
<dd><code><a href="../../../../../../../../org/apache/commons/math3/geometry/hull/ConvexHullGenerator.html#generate(java.util.Collection)">generate</a></code>&nbsp;in interface&nbsp;<code><a href="../../../../../../../../org/apache/commons/math3/geometry/hull/ConvexHullGenerator.html" title="interface in org.apache.commons.math3.geometry.hull">ConvexHullGenerator</a>&lt;<a href="../../../../../../../../org/apache/commons/math3/geometry/euclidean/twod/Euclidean2D.html" title="class in org.apache.commons.math3.geometry.euclidean.twod">Euclidean2D</a>,<a href="../../../../../../../../org/apache/commons/math3/geometry/euclidean/twod/Vector2D.html" title="class in org.apache.commons.math3.geometry.euclidean.twod">Vector2D</a>&gt;</code></dd>
<dt><span class="strong">Parameters:</span></dt><dd><code>points</code> - the set of input points</dd>
<dt><span class="strong">Returns:</span></dt><dd>the convex hull</dd>
<dt><span class="strong">Throws:</span></dt>
<dd><code><a href="../../../../../../../../org/apache/commons/math3/exception/NullArgumentException.html" title="class in org.apache.commons.math3.exception">NullArgumentException</a></code> - if the input collection is <code>null</code></dd>
<dd><code><a href="../../../../../../../../org/apache/commons/math3/exception/ConvergenceException.html" title="class in org.apache.commons.math3.exception">ConvergenceException</a></code> - if generator fails to generate a convex hull for
 the given set of input points</dd></dl>
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